Bottom Line:
The Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown.Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error.Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.

ABSTRACTThe Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons' positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.

f6-sensors-12-02561: 3DLocus beacons and virtual nodes configuration used in the test. (a) 3DLocus acoustic localization system; (b) Nodes configuration used in the test.

Mentions:
We apply the DSA method on a real ultrasonic LPS, where the assumptions of co-planarity between beacons and the presence of only Gaussian noise in the measurements are not completely true. We want to evaluate the performance of the method under non-ideal conditions. The test is performed on the 3DLocus system [4], shown in Figure 6(a), which is an acoustic LPS composed by n = 7 beacons deployed on a cell of 2.8 m × 2.8 m × 2.8 m. The calculated standard deviation of the distance measurements obtained with the 3DLocus is 0.23 mm, which is much more accurate than the one used in the simulations in Section 4. The height between the beacons and the virtual nodes is 1.4 m.

f6-sensors-12-02561: 3DLocus beacons and virtual nodes configuration used in the test. (a) 3DLocus acoustic localization system; (b) Nodes configuration used in the test.

Mentions:
We apply the DSA method on a real ultrasonic LPS, where the assumptions of co-planarity between beacons and the presence of only Gaussian noise in the measurements are not completely true. We want to evaluate the performance of the method under non-ideal conditions. The test is performed on the 3DLocus system [4], shown in Figure 6(a), which is an acoustic LPS composed by n = 7 beacons deployed on a cell of 2.8 m × 2.8 m × 2.8 m. The calculated standard deviation of the distance measurements obtained with the 3DLocus is 0.23 mm, which is much more accurate than the one used in the simulations in Section 4. The height between the beacons and the virtual nodes is 1.4 m.

Bottom Line:
The Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown.Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error.Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.

ABSTRACTThe Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons' positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.